If hyperbole and headlines scored goals, Edin Dzeko would have managed a debut hat-trick against Wolverhampton Wanderers but it was Carlos Tevez to whom Manchester City turned at the weekend. And although they won this battle, victory in the war looks set to elude them.

Tevez may have slipped into the shadows at Eastlands before this occasion, courtesy of the £27m acquisition of Dzeko, but he wrestled the limelight back after providing the crucial interventions on an afternoon that seemed to confirm the niggly feeling that City are not yet strong enough to win the title.

If it had been Manchester United or Arsenal tearing City apart as Wolves did in the first half an hour of this entertaining encounter then it could perhaps have been excused, but City were outplayed by a side who could only scrape an FA Cup draw against Doncaster Rovers in their previous match.

"We are growing every day but we still have to continuously work to improve," Tevez said. "We have to keep playing and winning matches, keep winning our points and trying not to drop points. And then that's when we can start thinking that we can win the championship."

A bright, energetic Wolves side could not believe their luck when it became apparent early on that City were playing like a pub team. Nenad Milijas's opening goal encapsulated the home side's ineptitude as Kolo Touré's clearance hit Vincent Kompany, which allowed Milijas to score from close in.

It was the very least Wolves deserved as Milijas, Kevin Doyle and Stephen Hunt played above themselves. City were the polar opposite – which ironically enough mirrored the respective clubs' positions in the league – although Kolo Touré did make amends with a deflected finish before half-time to equalise.

If City were to draw any comfort from an abject first half then it was the knowledge that they had undoubted class in their side – and undoubted class can only be kept quiet for so long, as Tevez proved. Unlike Wayne Rooney across town, Tevez has remained firmly in the goals since his contract shenanigans in December. Rooney was the 2010 forerunner for Tevez's manoeuvrings yet while the Englishman remains off the boil in terms of scoring, his former team-mate underlined he is anything but.

After 49 minutes and with the ball seemingly attached to his foot, Tevez wriggled through Christophe Berra, Hunt and Richard Stearman before brilliantly beating Wayne Hennessey to give City the lead and make the memories of those December days drift ever quicker over the horizon.

"It's been a long time since I scored a goal like that," Tevez said. "I am very happy here. The issue in the past is already in the past. I had my discrepancies with the boss but we spoke as two men and everything is solved and I am very happy. What I think and what I dream is to make history for this club. I am not thinking about this because of what I did for United, it's about what I can do for City."

City looked like they would kick on following Tevez's brilliant finish and that impression was exacerbated by a fine team goal started and finished by Yaya Touré, before a Tevez header made it 4-1 with 24 minutes left. Game over. Or maybe not.

Premier League-winning sides close matches out, they shut teams down and they strangle and pummel any remaining mental strength out of their opponents. Yet City did the opposite here and ended the game in the same desperate and listless manner as they had started it.

A Kevin Doyle penalty and Ronald Zubar's late header ensured a tense finish and although City's fans went home with the knowledge that they were top of the league, every ounce of their renowned scepticism will tell them they will not still be there come May. And for once, they will be spot on.

"We lost because they have that little Argentinian with great feet who has waltzed through our back four," Wolves' manager, Mick McCarthy, said after watching his side slip back into the relegation places. "But most teams would have laid down and had their backsides slapped at 4-1 down. It just shows what spirit the lads have got."